Last year's champion Shahjalal and runner-up Jibon Boli did not participate in this year's competition
Allegri led the Turin club to a Serie A-Italian Cup double in his first season in charge last term and also led them to the Champions League final where they lost to Barcelona.
He arrived at Juventus amid scepticism when he was appointed to replace Antonio Conte one year ago.
"Allegri is our leader and has enjoyed an extraordinary first season at the helm, taking the team to another level," club president Andrea Agnelli told reporters.
The coach also won Serie A with AC Milan in 2011 but was fired in January 2014 after a poor first half of the season.